Znd.Eng. Chem. Res. 1996,34, 1868-1872
1868
Phase Equilibria Prediction of Hydrogen Fluoride Systems from an Associating Model Ioannis G. Economout and Cor J. Peters* Laboratory of Applied Thermodynamics and Phase Equilibria, Faculty of Chemical Engineering and Materials Science, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands
Thermodynamic properties of hydrogen fluoride are strongly affected by the tendency of its molecules to form oligomers through hydrogen bonding in both the vapor and liquid phases. In this work, the associated perturbed anisotropic chain theory (APACT) is applied to correlate the vapor pressure and the saturated liquid and saturated vapor densities of pure hydrogen fluoride from the triple point up to the critical point with very good accuracy. An equilibrium model is used t o account for hydrogen bonding that assumes the formation of dimer, trimer, hexamer, and nonamer species. The model is used to predict the phase behavior of binary hydrogen fluoride mixtures with CFCs and HC1 and accurately describes the azeotrope formation of these systems. Liquid-liquid equilibria are predicted for several hydrogen fluoridefluorocarbon mixtures that have not been experimentally detected in the past.
Introduction Hydrogen fluoride is known to form molecular complexes through hydrogen bonding that considerably affect its thermodynamic properties. Several authors suggested the formation of cyclic hexamers of hydrogen fluoride in order to explain its vapor phase nonideal behavior (Simons and Hildebrand, 1924; Simons and Bouknight, 1932; Long et al., 1943; Jarry and Davis, 1953; Franck and Spalthoff, 1957). Beckerdite et al. (1983) examined various associating models for gaseous HF in the temperature range 293-330 K and concluded that a monomer-trimer-hexamer model best describes the experimental data. Redington (1982) used a continuum associating model that assumes the formation of oligomers of various sizes up to dodecamers for the vapor phase HF. Most of these models have been applied only for the vapor phase HF and only over a limited temperature range. In general, hydrogen bonding is usually much stronger in the liquid phase than in the vapor phase and so a model adequate for both phases should account for the liquid phase hydrogen bonding as well. In many cases, the monomer-hexamer model is applied in the liquid phase in order to describe the vapor-liquid equilibria of hydrogen fluoride mixtures (Gillespie et al., 1985; Wilson et al., 1989). Twu et al. (1993) developed an equation of state for hydrogen fluoride based on the Redlich-Kwong cubic equation of state and the monomer-hexamer equilibrium model. In order to correlate the vapor pressure data from the triple point up to the critical point, the model uses a function that has an unusual temperature dependence, and so the authors concluded that other oligomers besides hexamers should also be present in the pure hydrogen fluoride fluid. Recently, Lencka and Anderko (1993) presented an equation of state for hydrogen fluoride mixtures. The model is based on the combination of the PengRobinson cubic equation of state with an associating model. In this case, the infinite equilibrium model was used that assumes the formation of dimers, trimers, tetramers, etc. The equilibrium constant was made a function of the oligomer size using a Poisson-like
* To whom all correspondence
should be addressed.
Current address: Exxon Research and Engineering Company, P.O.Box 101, Florham Park, N J 07932. +
distribution function that results in a maximum value for the case of hexamer species. The model was shown to correlate accurately the phase equilibria of hydrogen fluoride-halocarbon mixtures. In this work, the associated perturbed anisotropic chain theory (APACT) is used to correlate the thermodynamic properties of pure hydrogen fluoride. A chemical equilibrium model is used for hydrogen bonding that assumes the formation of dimer, trimer, hexamer, and nonamer species. The equilibrium constant on a per bond basis is not constant for each of the chemical reactions unlike previous cases for other associating fluids like water and alcohols, where the equilibrium constant was independent of the oligomer size (Ikonomou and Donohue, 1986; Economou and Donohue, 1992). APACT is able to correlate with very good accuracy the saturated vapor and liquid densities and the vapor pressure of hydrogen fluoride from the triple point to the critical point. In addition, AF'ACT is used t o predict the phase equilibria of hydrogen fluoride mixtures with chlorofluorocarbons (CFCs), HC1, and water. The azeotrope between some of these binary mixtures is accurately predicted by the equation of state. In addition, AF'ACT is shown to predict limited miscibility between HF and two CFCs.
Model Development Hydrogen bonding between hydrogen fluoride monomers results in the formation of HF oligomers. In this model, it is assumed that dimers, trimers, hexamers, and nonamers are formed. Dimers are assumed to be linear (one hydrogen bond per dimer species) whereas trimers, hexamers, and nonamers are assumed t o be cyclic (three, six, and nine hydrogen bonds per species, respectively). The concentration of these species is a function of temperature and density. The concentration of dimer and trimer species is relatively high a t high temperature and low density (vapor phase at high temperatures). Hexamer species are favored at intermediate conditions (most of the pure HF experimental data fit in this range) whereas nonamer species are more favorable in the high-density region (liquid phase). In this way, the model is able to describe accurately the thermodynamic properties of pure hydrogen fluoride from the triple point (189.8 K) up to the critical point (461.2 K).
0888-5885/95/2634-186~~~9.oo/o 0 1995 American Chemical Society
[nd. Eng. Chem. Res., Vol. 34, No. 5, 1995 1869 The chemical equilibrium approach is used to describe the formation of these species:
i(HF) E? (HF),
i = 2,3, 6 , 9
1.0
0.8
(1)
Mathematically, these equilibria are expressed as
0.6
. 0
c
c‘ 0.4
where 4zis the fugacity coefficient and zi = nJnT is the mole fraction of component i. For convenience, an equilibrium constant can be defined on aper bond basis so that:
K i= Killi
i = 3, 6, 9 (3) = Ki = K. Per bond equilib-
For the dimer species, K’i rium constant values have been reported in the literature for the cyclic hexamer (Simons and Hildebrand, 1924; Long et al., 1943; Redington, 1982; Beckerdite et al., 19831, cyclic trimer (Beckerdite et al., 19831, and chain trimer (Redington, 1982). In this work, the per bond equilibrium constants are related to the equilibrium constant for the dimer species according to the following expressions based on the analysis by Lencka and Anderko (1993):
K3 = 1.71K213
K’6
= 4.6&16
K’g
0.2
0.0 10
10
10
10
10 KRTp
10
10
10
10
Figure 1. nT/no as a function of the “effective” strength of association, KRTe, from the one-site, two-site, three-site, and the new (HF)models.
where 0 is the molar density (in moVL), and so
= 6@” (4)
The associated perturbed anisotropic chain theory (APACT)is an equation of state that explicitly accounts for dispersion, polar, and hydrogen bonding interactions and has been applied extensively for phase equilibrium calculations of hydrogen bonding mixtures (Ikonomou and Donohue, 1986, 1988; Economou and Donohue, 1992). The equation of state is written in terms of the compressibility factor, 2, as
z = 1+ z a s s o c + Zrep + z a t t
(5) where Z”P and Zattare given by Vimalchand (1986) and Economou et al. (1995). Zassoc is the contribution t o the equation of state from hydrogen bonding and in general is calculated from the expression
The expression for nT/no is calculated from the material balances where no is the number of moles ignoring association and nT is the actual number of moles after association. For the case of pure HF, it is
By dividing both parts of eqs 7 and 8 by nT, one obtains two equations in terms of the mole fractions zi. These mole fractions can be expressed in terms of the equilibrium constants and the monomer mole fraction, 21, using eq 2 and the expression (Ikonomou and Donohue, 1986)
(9)
Equation 10 is solved numerically for n(m)l/no,and the result is substituted into eq 11t o calculate nT/no. The proposed association scheme accurately describes the experimental saturated density and vapor pressure data for pure hydrogen fluoride as discussed in detail in the following section. Other associating schemes were also applied to hydrogen fluoride, but the accuracy of such correlations was not very good. In Figure 1, nT/no is plotted as a function of the “effective” strength of association, KRTQ, from different association models. The one-site model describes best the carboxylic acids, the two-site model is suitable for alcohols, and the threesite model describes the water association (Ikonomou and Donohue, 1986; Economou and Donohue, 1992). It is obvious that the slope of nT/no from the new model is steeper than any of the other three models, and this behavior results in a better description of the experimental data. In addition, at high values of KRTQ hydrogen fluoride completely nonamerizes and so nT/ no 1/9. For mixtures of hydrogen fluoride with components that do not hydrogen bond (such as CFCs) the expressions for hydrogen bonding can be developed in a similar way. In the final expression equivalent to eq 10 for the mole fraction of HF monomers, the overall mole fraction of HF, xm, appears on the left-hand side of the equation instead of 1 whereas in the expression for nTIn0, the mole fraction of the second component, equal to 1- XHF, should be added to the right-hand side of eq 11.
-
Results and Discussion Pure Components. APACT with the associating model specifically developed for hydrogen fluoride has been applied t o describe the thermodynamic properties of this fluid. APACT is a five-parameter model for associating fluids. Three of the parameters account for
1870 Ind. Eng. Chem. Res., Vol. 34, No. 5, 1995 ".V
I"
-
,
200
250
300
350
400
,
500
450
'0
T(K1
T (Kl
60
0
Figure 3. Hydrogen fluoride monomer mole fraction along the saturation curve. APACT predictions.
tive to the nonassociating parameters, T* and u*. As a result, the associating parameters are fitted to the vapor density data, whereas T* and v* are fitted to the vapor pressure and liquid density data and are made temperature dependent in order to improve the agreement between experimental data and equation of state correlations. The following expressions are used for r" and
i
a zoj b
l0200
1
u*: 250
300
350
400
450
+ 1641.337T: 1+ 6.956T: 7.481 + 79.118T: u* = 1 + 7.592T:
r:=
500
TtK)
Figure 2. Experimental data (points) and APACT correlations (lines) for the saturated liquid and vapor volume (a, top) and vapor pressure of hydrogen fluoride (b, bottom) from the triple point (189.8K)up to the critical point (461.2K).
the nonassociating interactions: namely, T* is a characteristic dispersion energy parameter, u* is a characteristic size parameter, and c is the shape factor. In addition, there are two parameters that are used to calculate the equilibrium constant for association: the standard enthalpy of association, AH", and the standard entropy of association, AS". These parameters are calculated by fitting experimental liquid density and vapor pressure data. In the case of hydrogen fluoride, hydrogen bonding is very strong even in the vapor phase and so saturated vapor densities are used for the parameter regression as well. In summary, the following experimental data are used for the pure HF parameter regression: saturated vapor density from Jarry and Davis (1953) for T = 273.15-378.15 K and from Franck and Spalthoff (1957) for T = 383.15-461.15 K (critical point), saturated liquid density from Simons and Bouknight (1932) for T = 200-273.15 K, from Sheft et al. (1973) for T = 273.15-293.15 K, and from Daubert and Danner (1986) for T = 293.15-461.15 K, and vapor pressure from Daubert and Danner (1986) for T = 200461.15 K. Preliminary sensitivity analysis showed that vapor density calculations are most sensitive to the equilibrium constant for hydrogen bonding whereas liquid density and vapor pressure calculations are more sensi-
126.555
(12)
(13)
where T, = TIT,, T and r" are in K, and u* is in cm3/ mol. In this model, the hydrogen fluoride molecule is assumed to be spherical and so c is set equal to unity. The equilibrium constant K for the dimer formation is given by expression In K =
where AHa = -33.87 kJImol, AS"IR = -15.37, ACp"IR = 6.05, and TO = 298.15 K. In APACT, for other associating fluids such as water, alcohols, and carboxylic acids, ACp"IR = 0. Polar interactions due to the HF dipole moment were not taken into account in the model. With these parameters, APACT is able to correlate the experimental saturated liquid and vapor volumes and the vapor pressure very accurately from the triple point up to T, = 0.99. The percentage average absolute deviation (% AAD) between experimental data and AF'ACT correlations is 2.5% for vapor pressures, 0.7% for liquid volumes, and 0.2% for vapor volumes. In Figure 2, comparisons are shown between experimental data and APACT correlations. In Figure 3, the monomer mole fraction (21= n l l n ~along ) the saturation curve is shown as predicted from the model. Association is very strong in the liquid phase especially at low tem-
Table 1. APACT Pure Component Parameters for the Compounds Examined in This Work and Percentage Average Absolute Deviation (% AAD) between Experimental Data and APACT Correlations for the Saturated Liquid Volume and VaDor Pressure for the TemDerature Range Indicated
R12a R22a R113a HCl a
260.6 245.1 324.7 229.2
45.01 35.01 66.35 19.26
Parameters taken from Blindenbach et al. (1994).
1.475 1.492 1.605 1.056
1.386 1.546 0.200 2.630
203-373 183-363 283-323 180-300
0.847 1.016 1.960 1.360
203-363 173-333 283-323 180-300
Ind. Eng. Chem. Res., Vol. 34, No. 5, 1995 1871 Table 2. Experimental Dipole Moments and Average Molecular Polarizabilities (CRC Handbook, 1992)and Dispersion Energy Parameters for the Components Examined in This Work component
dipole moment (D)
R12 R22 R113a HC1
0.51 1.42 0.48 1.08
a (A3)
d k (K)
2.63
118 140 118 150
I
I
".?\
~~
peratures, and so ZIis small (21 is lower than 0.01 below 300 K). Hydrogen bonding is also relatively strong in the vapor phase and so z1 is well below unity. A temperature increase results in less hydrogen bonding in both phases, and so ZIincreases, but at temperatures close to the critical point liquid-like densities in the vapor phase result in a decrease of the monomer mole fraction in the vapor phase. For mixture calculations, the dispersion energy parameter d k for pure components is needed. In the case of HF, q which is the normalized external surface area per molecule is calculated from the expression
"h I
T = 298.15 K
!
4-
'
I
2-
0.0 R 22
0.2
66
0.4 X,
0.8
Y
10 HF
Figure 4. Experimental data (points) and APACT predictions (solid lines) and correlations (dashed lines) of the R22-HF phase equilibria at 258.15 and 298.15 K.
23 LLE
21
(15) where
U * C H ~=
10.699 cm3/mol,qCHz = 1, and so
The APACT parameters for the other components examined in this work were calculated by fitting experimental liquid density and vapor pressure data. These parameters are shown in Table 1together with the % AAD between experimental data and APACT correlations. In Table 2, the experimental dipole moment, the experimental average molecular polarizability, and the dispersion energy parameter for the various components are shown. Binary Mixtures. Hydrogen fluoride is a very difficult compound to deal with, and so despite its industrial importance for several processes the experimental data available for hydrogen fluoride mixtures are limited. In this work, all the experimental binary mixture data available in the literature were correlated by APACT. In Table 3, the hydrogen fluoride systems examined in this work are summarized. The range of temperatures where experimental data are available is shown together with the % AAD between experimental data and APACT calculations for the bubble pressure. Two different types of calculations were performed. In the first case (the so-called prediction) no binary adjustable parameters were used and calculations were based purely on pure component parameters. In the second case, a temperature-independent binary adjustable parameter (kg) was used in order to obtain the best agreement between experiments and calculations. APACT predictions are in good agreement with the experimental data, and also ku is very small so that APACT predictions can be reliable for systems where no experimental data are available. In Figure 4, experimental data (Wilson et al., 1989) and APACT calculations are shown for the binary mixture R22 (CHClF2)-HF a t 258.15 and 298.15 K. Azeotrope formation at both temperatures is accurately predicted by the model. In addition, at 258.15 K, APACT predicts a region of limited miscibility between the two components in the composition range XHF = 0.406-0.753. Wilson et al. (1989) also indicated that
0.0 R 113a
0.2
04
06 X
0.8
10 HF
Figure 5. Experimental data (points) and APACT predictions (lines) of the R113a-HF phase equilibria at 383.15 K. Table 3. Binary Hydrogen Fluoride Mixtures Examined in This Work. % AAD between Experimental Data and APACT Calculations. Predictions Are Performed without Any Binary Adjustable Parameter (k" = 0) Whereas for Correlations a Temperature Independent k" Was Used %AAD predic- correlamixture T(K) tion tion kU data source R22-HF 258-298 5.5 1.6 -0.014 Wilson et al., 1989 R113a-HF 383 5.7 5.7 0.00 Knappet al., 1991 HC1-HF 244 9.3 3.9 -0.019 Gillespie et al., 1985
there is a region of limited miscibility for this system, and using Wilson's equation we estimated the lilnited composition to be in the region XHF = 0.069-0.526. In Figure 5 , experimental data (Knapp et al., 1991) and APACT predictions are shown for the binary mixture R113a (CC13CFd-HF at 383.15 K. APACT predicts a vapor-liquid-liquid equilibrium (VLLE)line at 18.5 bar and a liquid-liquid equilibrium (LLE)region above 18.5 bar. LLE for this system has been also suggested by Lencka and Anderko (1993). No experimental data are available to verify this prediction. We attempted to investigate the LLE of R12 (CC12F2)HF and R22-HF mixtures with respect to temperature. In Figure 6, APACT predictions are shown for these two mixtures. No experimental data are available for this type of phase equilibria. At low temperatures, the region of limited miscibility increases. At these conditions, the hydrogen fluoride self-association is very strong and so hydrogen fluoride molecules exclude CFC molecules from their immediate neighborhood resulting in the formation of two liquid phases. As the temper-
1872 Ind. Eng. Chem. Res., Vol. 34, No. 5, 1995 1
I .
00
0.2
0.6
0.4
R 12/R22
0.8
10
HF
X, Y
Figure 6. APACT predictions ofthe R12-HF and R22-HF LLE. I
h
10
1
0.0 HCI
I
I
0.2
06
0.4 X,
0.8
1.0 HF
Y
Figure 7. Experimental data (points) and APACT predictions (solid lines) and correlations (dashed lines) of the HC1-HF phase equilibria a t 244.15 K.
ature increases, dispersion interactions between unlike molecules as well as entropic contributions become relatively important and so the two components eventually become completely miscible. The region of limited miscibility is much larger for the mixture of the less polar R12 @ = 0.51 D) compared to the mixture containing the more polar R22 @ = 1.42 D) which is physically realistic since HF molecules prefer to be in a polar environment rather than in a nonpolar one. In fact, for the case of R23-HF mixture, where R23 has a dipole moment of 1.65 D, APACT predicts that the two components are completely miscible over the entire temperature range. In Figure 7, experimental data (Gillespie et al., 1985) and APACT calculations are shown for the HF-HC1 mixture a t 244.15 K. APACT is able to correlate accurately the equilibrium pressure as well as the vapor phase composition.
Conclusions In this work, an associating model was developed to describe the thermodynamic properties of hydrogen fluoride based on the associated perturbed anisotropic chain theory (APACT). The very accurate description of the properties of pure hydrogen fluoride results in accurate phase equilibria predictions of systems containing HF, CFCs, and HCI. Measurements are needed in order to verify some of the model predictions, especially the limited miscibility between HF and various CFCs.
Literature Cited Beckerdite, J. M.; Powell, D. R.; Adams, E. T. Self-Association of Gases. 2. The Association of Hydrogen Fluoride. J . Chem. Eng. Data. 1983,28, 287-293. Blindenbach, W. L.; Economou, I. G.; Smits, P. J.; Peters, C. J.; Swaan Arons, J. de. Modelling the Thermodynamic Properties of CFC and HCFC Compounds and the Vapor-Liquid Equilibria of CFC and HCFC Mixtures and CFC/HCFC-Hydrocarbon Mixtures with the Perturbed-Anisotropic-Chain-Theory (PACT). Fluid Phase Equilib. 1994, 97, 13-28. CRC Handbook of Chemistry and Physics, 73rded.; CRC Press: Boca Raton, FL, 1992. Daubert, T. E.; Danner, R. P. Physical and Thermodynamic Properties of Pure Chemicals. Data Compilation, DIPPR; AIChE: New York, 1986. Economou, I. G.; Donohue, M. D. Equation of State with Multiple Associating Sites for Water and Water-Hydrocarbon Mixtures. Ind. Eng. Chem. Res. 1992,31,2388-2394. Economou, I. G.; Peters, C. J.; Swaan Arons, J. de. Water-Salt Phase Equilibria at Elevated Temperatures and Pressures: Model Development and Mixture Predictions. J . Phys. Chem. 1995,99,6182-6193. Franck, E. U.; Spalthoff, W. Fluonvasserstoff I. Spezifische Warme, Dampfdruck und Dichte bis zu 300 "C und 300 at. (Hydrogen Fluoride. I. Specific Heat, Vapor Pressure, and Density up to 300 "C and 30 atm.) 2.Elektrochem. 1957, 61, 348-357. Gillespie, P. C.; Cunningham, J. R.; Wilson, G. M. Vapor-Liquid Equilibrium Measurements for the Hydrogen Fluoride/Hydrogen Chloride System. AIChE Symp. Ser. 1985, 81 (244), 4148. Ikonomou, G. D.; Donohue, M. D. Thermodynamics of HydrogenBonded Molecules: The Associated-Perturbed-AnisotropicChain-Theory. AIChE J . 1986,32, 1716-1725. Ikonomou, G. D.; Donohue, M. D. Extension of the AssociatedPerturbed-Anisotropic-Chain-Theory to Mixtures with More than One Associating Component. Fluid Phase Equilib. 1988, 39, 129-159. Jarry, R. L.; Davis, W. The Vapor Pressure, Association, and Heat of Vaporization of Hydrogen Fluoride. J . Phys. Chem. 1953, 57, 600-604. Knapp, H.; Walz, R.; Wanzke, W. Herstellung Halogenierter Kohlenwasserstoffe: Prozessgestaltung und Thermodynamische Grundlagen zur Auslegung; Deutsche Ktilte-Klima-Tagung: Berlin, Germany, 1991. Lencka, M.; Anderko, A. Modeling Phase Equilibria in Mixtures Containing Hydrogen Fluoride and Halocarbons. AIChE J . 1993,39,533-538. Long, R. W.; Hildebrand, J. H.; Morrell, W. E. The Polymerization of Gaseous Hydrogen and Deuterium Fluorides. J . Am. Chem. SOC.1943, 65, 182-187. Redington, R. L. Nonideal-Associated Vapor Analysis of Hydrogen Fluoride. J . Phys. Chem. 1982,86, 552-560. Sheft, I.; Perkins, A. J.; Hyman, H. H. Anhydrous Hydrogen Fluoride: Vapor Pressure and Liquid Density. J . Inorg. Nucl. Chem. 1973,35,3677-3680. Simons, J. H.; Hildebrand, J. H. The Density and Molecular Complexity of Gaseous Hydrogen Fluoride. J . Am. Chem. SOC. 1924,46, 2183-2191. Simons, J. H.; Bouknight, J. W. The Density and Surface Tension of Liquid Hydrogen Fluoride. J . Am. Chem. SOC. 1932,54,129135. Twu, C. H.; Coon, J. E.; Cunningham, J . R. An Equation of State for Hydrogen Fluoride. Fluid Phase Equilib. 1993,86,47-62. Vimalchand, P. Thermodynamics of Multipolar Molecules. The Perturbed-Anisotropic-Chain-Theory. sen: Ph.D. Dissertation, The Johns Hopkins University, Baltimore, MD, 1986. Wilson, L. C.; Wilding, W. V.; Wilson, G. M. Vapor-Liquid Equilibrium Measurements on Six Binary Mixtures. AIChE Symp. Ser. 1989, 85 (271), 51-74.
Received for review August 15, 1994 Revised manuscript received January 20, 1995 Accepted February 6, 1995@ IE940492M @
Abstract published in Advance ACS Abstracts, March 15,
1995.
